33. Let X and Y be independent exponential random variables with respective rates and . (a) Argue that, conditional on , the random variables

33. Let X and Y be independent exponential random variables with respective rates λ and μ.

(a) Argue that, conditional on , the random variables and are independent.

(b) Use part

(a) to conclude that for any positive constant c

(c) Give a verbal explanation of why and are (unconditionally) independent.